A Note on the Security Number of Grid-Like Graphs

Abstract

For any graph $G=(V,E)$, a non-empty set $S\subseteq V$ is $secure$ if and only if $|N[X]\cap S|\ge |N[X]–S|$ for all $X\subseteq S$. The cardinality of a minimum secure set in $G$ is the security number of $G$. In this note, we give a new proof for the $securitynumber$ of grid-like graphs.